Elastic wave propagation in triangular chiral lattices: Geometric frustration behavior of standing wave modes

Abstract

The paper presents an investigation of elastic wave propagation in triangular chiral lattices composed of zigzag beams. Considerable attention is focused on the formation of band gaps, where a wave with specific frequency is forbidden from passing through the material. Band structure analysis reveals that compared with the conventional triangular configuration with straight cell walls, the emerging band gaps are characterized by their upper bounding modes performing rotational deformation shapes. Owing to the geometric constraint of the triangle topology, the symmetric rotation standing mode, which is present in the band gap edges of both hexagonal and square chiral honeycombs, is frustrated into a complex deformation pattern, leading to a higher band-gap edge frequency for the triangular chiral lattices. Meanwhile, the natural frequency of the simple heuristic model, a cell wall with two ends simply supported, also fails to predict the bounding frequency corresponding to the frustrated standing mode. A modified heuristic model is constructed according to the free vibration analysis of a triangular frame, which provides a rotation relationship with regard to the three junctions, i.e., the sum of the rotational angles is zero. The natural frequency of the modified heuristic model provides an accurate estimation of the band frequency of the geometrically frustrated standing mode. Our findings illustrate the geometric frustration phenomenon with respect to elastic wave propagation in triangular periodic lattices, which is beneficial for the band gap width enhancement, thus facilitating vibration suppression.